The generator matrix

 1  0  0  1  1  1  X  1  1  X  1  X  1  0  1  1  1  1  1
 0  1  0  0  1 X+1  1  X X+1  1  0  0  1  1  X  X  X  0  0
 0  0  1  1 X+1  0 X+1  1 X+1  X  X  1  X  1 X+1 X+1  1  1  0
 0  0  0  X  X  X  0  0  0  X  X  X  0  X  X  0  X  X  0

generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+17x^16+32x^17+20x^18+16x^19+12x^20+8x^21+4x^22+2x^24+8x^25+8x^26

The gray image is a linear code over GF(2) with n=38, k=7 and d=16.
As d=16 is an upper bound for linear (38,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.1 seconds.